弱凸向量優(yōu)化問題的最優(yōu)性條件

王彩玲, 高慧巖

(1. 吉林大學(xué) 數(shù)學(xué)學(xué)院, 長春 130012; 2. 北京中科金財(cái)科技股份有限公司, 北京 100083)

文獻(xiàn)[1-6]利用抽象次微分對(duì)單目標(biāo)規(guī)劃問題進(jìn)行了研究. 本文利用抽象次微分給出目標(biāo)函數(shù)為弱凸函數(shù)的向量優(yōu)化問題的最優(yōu)性條件, 推廣了文獻(xiàn)[1-6]的結(jié)果.

1 抽象凸函數(shù)的概念

考慮如下多目標(biāo)規(guī)劃問題：

?x∈Rn}.

?x∈Rn}.

2 最優(yōu)性條件

證明： 首先, 證明

其次, 證明

由于

(1)

又因?yàn)?/p>

(2)

(3)

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